# Addition facts

An addition fact, also referred to as a number bond, is a basic addition problem that is meant to serve as a foundation for learning addition. It is made up of the sum of two addends (usually from 1-10). Below are some examples of addition facts:

3 + 4 = 7

2 + 9 = 11

8 + 7 = 15

The purpose of teaching addition facts is to make them so familiar that given any 2 numbers in an addition fact, a child can quickly recognize the addition fact and identify the remaining number. Once a child is comfortable with the addition facts, they can be used as a way to learn about or solidify their understanding of other arithmetic operations. For example, the following addition fact can be used to show the relationship between addition and subtraction.

10 + 2 = 12

Given that the above addition fact is known, it can be used to introduce subtraction as:

12 - 2 = 10

Similarly, repeated addition can be used as an introduction to multiplication. For example, given that a child knows the addition facts 5 + 5 = 10 and 10 + 5 = 15, we can equate the addition problem, 5 + 5 + 5 = 15, to the multiplication problem, 5 × 3 = 15.

## Learning/practicing addition facts

One way to learn or practice various addition facts is by using a table of addition facts. Below is a table that can be used to find the sum of the various combinations of the numbers 1-10. 0 is not included in the table since adding 0 to any number results in that same number.

To use the table, pick two addends, one from the grey row and one from the column. Determine where their respective row and column intersect to find their sum. It doesn't matter whether an addend is chosen from a row first or a column first, but for the following examples, the addends are chosen first from the row, then the column. The solutions to the following examples are highlighted in the table.

10 + 2 = 12

3 + 5 = 8

9 + 8 = 17

+ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |

10 | 11 | 12 | 13 | 14 | 15 | 17 | 17 | 18 | 19 | 20 |

Since a table like this can be used to determine the solution to any addition fact in the table relatively quickly, it is useful for looking up addition facts a student may be unsure about until all the facts become familiar. When first starting to learn addition, the table can be broken up in various ways. For example, a student could choose to focus on learning all the facts for the the first few rows (or columns), then continue adding more rows until they know all of the addition facts in the table.

Another way to learn or practice various addition facts using a table is to write out rows and columns up to the desired numbers then fill in the rest of the table, referencing a completed table as needed. This may also help with developing an ability to recognize the patterns in a table.

The table can also be made to include more or fewer than the first 10 numbers. For example, starting with smaller subsets of the table, such as the sum of all the combinations of the numbers 1-5, or all the combinations of numbers that add to 20, can make the table seem less daunting to begin with.